Abstract
The iterative k-variable means, i.e. the means of the form where f maps a real interval I into itself, is the ith iterate of f, and are real numbers, are considered. Reflexivity of such a mean reduces to a polynomial type iterative functional equation. The conditions under which is a mean and a strict mean are given. In the case the invariance of the quasi-arithmetic mean with respect to the iterative mean-type mappings are considered and, as an application, some functional equations are effectively solved. Possible generalizations are mentioned.
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